Please Refer the Below Sample code for your referance.
HTML
<form id="form1" runat="server">
<asp:TextBox ID="txtDate" runat="server" ReadOnly="true"></asp:TextBox>
<asp:Button ID="btnSubmit" runat="server" Text="Submit" OnClick="btnSubmit_Click" />
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.6/jquery.min.js" type="text/javascript"></script>
<script src="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8/jquery-ui.min.js"
type="text/javascript"></script>
<link href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8/themes/base/jquery-ui.css"
rel="Stylesheet" type="text/css" />
<script type="text/javascript">
$(function () {
$("[id*=txtDate]").datepicker({});
});
</script>
</form>
Code
protected void btnSubmit_Click(object sender, EventArgs e)
{
string dt = Request.Form[txtDate.UniqueID];
if (string.IsNullOrEmpty(dt.Trim()))
{
ClientScript.RegisterStartupScript(this.GetType(), "Alert", "alert('Please select date');", true);
}
}